The amount of time that people spend at Grover Hot Springs is normally distributed with a mean of 62 minutes and a standard deviation of 18 minutes. Suppose one person at the hot springs is
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A
![The amount of time that people spend at
Grover Hot Springs is normally
distributed with a mean of 62 minutes
and a standard deviation of 18 minutes.
Suppose one person at the hot springs is
randomly chosen. Let X = the amount of
time that person spent at Grover Hot
Springs . Round all answers to 4 decimal
places where possible.
a. What is the distribution of X? X ~ N(
b. Find the probability that a randomly
selected person at the hot springs stays
longer then 75 minutes.
c. The park service is considering
offering a discount for the 4% of their
patrons who spend the least time at the
hot springs. What is the longest amount
of time a patron can spend at the hot
springs and still receive the discount?
minutes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7e704f02-28f6-4731-8e0d-307f5cf3c60b%2F82f4d595-9d1c-4da7-b7c5-19084806091c%2Fl0rpdhi_processed.jpeg&w=3840&q=75)
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